Optimal shape design of the film-coupled nanoparticle using the phase field design method

Localized surface plasmon resonance (LSPR) occurs when an electromagnetic (EM) wave hits a metal nanoparticle. The interaction between a gold (Au) nanoparticle and a thin metal film produces a strong EM wave called as LSPR at the small gap between the nanoparticle and the film. The field strength of the LSPR increases dramatically as the distance between the Au nanoparticle and the film decreases. In this study, we focus on the field enhancement at the small gap by obtaining the appropriate shape of the Au nanoparticle. Since the shape or the size of a nanoparticle to enhance the LSPR is hard to be determined theoretically, the structural optimization method based on the phase field method is employed to design the shape of the nanoparticle. To obtain reliable results taking the small gap of 2 nm into account, we proposed a new filtering scheme based on a smoothed Heaviside function and applied it to nanoparticle design.